(Preprint) AAS 19-724 TRANSFER TRAJECTORY OPTIONS FOR SERVICING SUN-EARTH-MOON LIBRATION POINT MISSIONS David C. Folta* and Cassandra Webster1 Future missions to the Sun-Earth Libration L1 and L2 regions will require scheduled servicing to maintain hardware and replenish consumables. While there have been statements made by various NASA programs regarding servicing of vehicles at these locations or in Cis-lunar space, a practical transfer study has not been extensively investigated in an operational fashion to determine the impacts of navigation and maneuver errors. This investigation uses dynamical systems and operational models to design transfer trajectories between the Sun-Earth Libration region (QuasiHalo orbit) and the Earth-Moon vicinity (Distant Retrograde Orbit, QuasiHalo Orbit, Halo Orbit, and Near Rectilinear Halo Orbit). We address the total ΔV cost of transfers and operational considerations between each pair of locations using a Monte Carlo analysis. INTRODUCTION Future missions to the Sun-Earth Libration L1 and L2 regions will require scheduled servicing to maintain hardware and replenish consumables. While there have been statements made by various NASA programs regarding servicing of vehicles at these locations or in Cis-lunar space, a feasibility study of transferring these vehicles has not been extensively investigated in an operational fashion. (1,2,3,4) The design of the related transfer trajectories between locations are dependent on orbit types and their dynamical system properties, departure and arrival conditions, and the servicing vehicle’s capabilities. Sun Earth-Moon Libration science missions will accommodate multiple orbit types, from large QuasiHalo to smaller Lissajous. Initial orbit conditions considered here are based on upcoming missions such as the Wide-Field Infrared Survey Telescope (WFIRST). The servicing vehicle is assumed to be in the Earth-Moon vicinity and this investigation provides trajectory designs of transferring the servicing vehicle from the Earth-Moon region or proposed Gateway orbit to the Sun-Earth L2 (SEL2) region, and transferring the mission spacecraft from SEL2 back to the Earth-Moon vicinity. The analysis done in this paper begins with a dynamical systems approach as an initial strategy. Then using numerical computation with high fidelity models and linear and non-linear targeting techniques, the various maneuvers and ∆V’s associated with each orbit and related transfer are computed. From a dynamical system standpoint, we speak to the nature of these orbits and their stability. The existence of a connection between unstable regions, such as manifolds between the Earth-Moon and Sun-Earth Libration point systems, enables mission designers to envision * Senior Fellow, Aerospace Engineer, NASA Goddard Space Flight Center, Greenbelt, MD, 20771, [email protected] 1 WFIRST Flight Dynamics Lead, NASA Goddard Space Flight Center, Greenbelt, MD, 20771, [email protected] . 1 scenarios of multiple spacecraft traveling economically from system to system, rendezvousing, servicing, and refueling along the way. We address the cost of transfers between each pair of locations. Early analysis suggests these transfer ΔV costs can range from centimeters per second for the more unstable orbits to nearly tens or possibly hundreds of meters per second for the stable co-linear locations.(5,6) Of course ΔV cost depends on several parameters, such as orbit amplitudes (as measured in a rotating, libration centered coordinate system), mis-modeled accelerations due to solar radiation pressure and third body gravity, the calibration of the propulsion system, and the accuracy of the navigation solutions. Additionally, the location in the respective orbits and overall timing play a major role in being able to establish these transfers. Our analysis incorporates these errors and timing considerations in non-linear control efforts to estimate the transfer cost. To determine feasible designs across various dynamical regions, several tools are employed which are grounded in the dynamical properties of the science orbits and maintenance regions as well as the dynamics of their transfers. These tools include the Goddard and Purdue developed software tool, Adaptive Trajectory Design (ATD), used to model dynamical systems and to represent natural transfer manifolds, and AGI’s STK® software to design transfers in a high fidelity environment. The results of this paper provide an assessment of possible transfers, highlighting the total ΔV due to navigation and maneuver uncertainties, their transfer durations, orbit geometry influences, and other trajectory parameters of interest. EARTH-MOON AND SUN-EARTH ORBIT EXAMPLES For this study, the servicing vehicle is assumed to be in the Earth-Moon vicinity and the orbits that are considered in this analysis include a planar Lunar Distant Retrograde Orbit (DRO), Earth- Moon L2 Halo and QuasiHalo orbits, and the proposed Lunar Gateway Near Rectilinear Halo Orbit (NRHO). Earth-Moon L1 orbits were not included in this study because transfers between Earth- Moon L2 (EML2) and Earth-Moon L1 have been operationally demonstrated in 2012 by the Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon’s Interaction with the Sun (ARTEMIS) mission. (7) Current considerations for servicing are focused only on the above orbit types due to assumptions of V cost and transfer trajectory requirements. Figures 1 through 5 present the orbits used in this analysis and Table 1 presents the Cartesian components in their respective coordinate frames and dynamical systems parameters for each orbit. The Jacobi Constant (JC) is measured in the respective orbit system, e.g. SEL2 or EML2 and the stability index (SI) is the stability of the system and indicates the need for stationkeeping as well as the ease of departure from or insertion into these orbits. As the SI approaches a value of ‘1’, the orbit becomes more stable. While this is a benefit for stationkeeping, it also means that the ΔV required to depart will increase. Figures 1 through 3 show the Earth-Moon orbits (NHRO, DRO, Halo, and QuasiHalo) while Figure 4 shows the principal WFIRST SEL2 QuasiHalo orbit design used for this analysis. The Earth-Moon L2 Halo orbit shown was constructed to represent a minimum shadow orbit and, in this case, provides shadow free orbits for more than a year at a time. The EML2 QuasiHalo and DRO are of the Lyapunov type to compare to Halos which have an out- of-plane component resulting in additional departure or insertion constraints and ΔVs for alignment of the transfer to or from SEL2. Lastly, a NRHO was simulated based on the proposed Gateway orbit.(8) All orbits were generated using an initial epoch date of January 1st, 2030. This date was chosen to reflect the possible timeline of such servicing missions and provides feasible launch opportunities for the transfers to and from the servicing regions. In a concluding section, we discuss the transfer design differences starting from the above Earth-moon locations to either the principal WFIRST QuasiHalo orbit or to a large SEL2 Lissajous orbit which is also deigned to meet WFIRST orbit requirements. This comparison provides a basis 2 for the transfer cost and insertion cost into both orbit types and allows one to determine if the correction maneuvers are similar. Table 1. Orbit Parameters, Maximum Values Orbit X Amplitude Y Amplitude Z Amplitude SI* JC* Comment Approx (km) (km) (km) U/S Orbit Period (day) EML2 Halo -14608 37246 -11382 1172 3.2 Minimum 15 (EML2) Shadow EML2 -21618 46212 0 947 3.1 ARTEMIS 15 (EML2) QuasiHalo type Lunar DRO -132353 -91663 0 1 2.9 Small 13 (moon) amplitude DRO NRHO -67133 17216 -70051 1.5 3.0 Gateway 7.2 (moon) (Gateway) design QuasiHalo -281891 721222 -244395 1536 3.0 WFIRST 180 SEL2 selected (SEL2 ) (WFIRST) orbit Lissajous 206887 542200 444011 1500 3.0 Shadow 180 SEL2 Free design (SEL2 ) *Approximate values based on ATD constructed orbits Initial Transfer Designs Once the proposed servicing vicinity and prime mission orbits were selected, the task then turned to the initial design of the transfer orbits. The transfers considered here are designed to minimize (not optimize) the total ΔV and transfer duration by using the natural dynamics in the Earth-Moon and Sun-Earth regions. The idea behind this process was to rely on the natural motion and the software tools developed over the last several years to construct such orbits. The initial transfers that provide the guidance on where to place departure and arrival maneuvers are based on dynamical systems within the ATD tool (9) to find the natural trajectories to transfer between the two regions of interest. Figure 1. Halo, QuasiHalo, DRO, and NRHO in Figure 2. Halo, QuasiHalo, DRO, and NRHO in Rotating Coordinates, view from EML2 +Z axis Rotating Coordinates, view from EML2 -Y axis Figure 2. Halo, QuasiHalo, DRO and NRHO in Rotating Coordinates view from EML2 -Y 3 axis Figure 3. Halo, QuasiHalo, DRO and NRHO in Figure 4. WFIRST SEL2 Orbit, in Rotating Rotating Coordinates, view from EML2 +X axis Coordinates, view from SEL2 +Z axis ATD is an original and unique concept for quick and efficient end-to-end trajectory designs using proven piecewise dynamical methods. ATD provides mission design capabilities of cis-lunar, Earth-Moon, and Sun-Earth orbits within unstable/stable regions through the unification of individual trajectories from different dynamical regimes. Based on a graphical user interface, ATD provides access to solutions that exist within the framework of the Circular Restricted Three Body Problem in order to facilitate trajectory design in an interactive and automated way. ATD was developed under the Fiscal Year 2012 and 2013 NASA GSFC Innovative Research and Development programs. Other mission design approaches using commercial and NASA software tools, such as AGI’s STK/Astrogator ® and Goddard’s open source General Mission Analysis Tool (GMAT), complete each trajectory design phase in isolation with the beginning/end state information from one regime used to kick-off the design process in the next regime.